----- Original Message ----- From: "Justin Schwartz" <jkschw at hotmail.com>
>
> >Sorry, the question is whether Hegel's Logic is consistent. See
> >Bertrand Russell and the Brit rejection of Hegelianism on that one.
> >Completeness is out for any system of logic that incorporates
simple
> >arithmetic.
> >
> >%%%%%
> >
> >CB: Isn't Hegel famous for Logic with contradiction at the center ?
Did
> >Russell really solve his paradox ?
> >
>
> Goedel's incompleteness theorum has nothing to do with Hegel or
> contradiction. The theorem states that in any formal that is
powerful enough
> to formulate simple arithemetic, there is at least one true
proposition that
> cannot be proved within that system. The theorem shows that
arithmetic
> cannot be reduced to logic. It does not show that logically
incompatible
> propositions are true. As for Hegel, he did not posit that they
could. His
> notion of contradiction is not logical, but ontological. It is a
misleading
> effect of the development of the use of words that we use the term
"logic"
> to describe the properties of formal systems, while Hegel used it to
> describe metaphysics. He was concerned with the nature of reality;
logic, as
> normally used, is not. In the context of Hegel's logic, a
contardiction is a
> dynamic instability in a phenomenon that makes it tend to change
into a
> phenomenon with a different nature and character. It is not an
asserion that
> p & not-p, as an ordinary logical contradiction is. jks
>
===============
If I remember right, I posted something about Hegel's appropriation of contradiction from Leibniz' corpus and their shared fascination with Chinese and Indian approaches to ontology and logic.
What I was trying to get at was that network of assertions in Logic themselves don't meet the requirements of logical rigor as we understand them today; that is, it's got a lot of contradiction and rhetoric in the text. That Marx appropriated the notion of contradiction to describe 19th century capitalism and the dynamics of social conflict was brilliant, no doubt, but for avoiding misunderstandings why don't we just say irreconcilable antagonisms or destabilizing social conflicts or conflicting motivations of agents in the market etc.?
As for logically incompatible propositions, there's been loads of work done in temporal logic, mereology, paraconsistent logic, fuzzy logic and the like just over the last 20 years that renders alethic propositions, dialethic propositions and tu quo quo arguments interesting again. One person who's done some real interesting stuff is Graham Priest.
< http://www.ifs.csic.es/sorites/Issue_07/item5.htm >
We won't even go into whether there's a logic to randomness a la Gregory Chaitin.............
Ian